THE ASTRONOMICAL VIEW OF NATURE. 335 



quantities and in varying combinations. That a smaller 

 quantity of matter in motion could produce the same 

 action as a larger which was moving slowly, or even 

 apparently at rest, and acted only by what is termed its 

 dead-weight, was a well-known phenomenon ; but it was 

 only within the half-century which preceded the publica- 

 tion of the ' Principia ' that, through the labours of Galileo 

 and of Hnygens, mathematical definitions and simple 

 formulae were laid down, and generally accepted, which 

 gave the means of accurately measuring and calculating 

 the phenomena of moving bodies and the combination of 

 forces. These labours resulted in a definition of matter 

 which, translated into the language of our day, says that 

 matter is that which moves and is capable of resisting 

 any change of motion. Motion is a measurable quan- 

 tity. For its measurement we require the measurement 

 of space and time, and the well-known relation of both 

 viz., velocity. 



The above formula therefore says that matter is mea- 

 sured by the resistance it offers to change of motion or 

 of velocity. And correspondingly force is that which is 

 capable of producing change of motion, or velocity in 

 matter, and it is measured by the amount of change it 

 produces. Given a definite, though unknown, force, 

 portions of matter i.e., masses can be compared by the 

 resistance they offer to the change of their motion ; the 

 smaller the change the larger the mass or quantity of 

 matter. Given a definite, though unknown, quantity of 

 matter, forces can be measured by the different changes 

 they produce in the motion i.e., the velocity of this 

 quantity ; they are greater or smaller in the proportion 



